The somewhat counterintuitive answer is that it actually is statistically better to go for the marble in the bag instead of the one in your hand. It took about 45 minutes for this *$#! young fellow to convince me of this.
Here's why it's true:
When you take the marble from the bag, you have a 1 in 3 chance of choosing the black marble. That means there is a better chance that it is in the bag (2 in 3 chances) than in your hand. So far so good. Well, if this little know-it-all kid, shows you one of the marbles in the bag that ISN'T the black one, there is still a 2 in 3 chance that the black marble is in the bag, but now all that chance is tied up in the one marble that remains in the bag... so you should take it rather than the 1 in 3 chance marble you are holding in your hand.